Theory and Design of Audio Rooms-Reformulation of Sabine Foroula

Authors : Dr. Ismail Abbas

Volume/Issue : Volume 6 - 2021, Issue 10 - October

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Sabine's semi-imperial formula, sometimes referred to as Sabine's theory, proposed a century ago, remains the main formula for calculating RT reverberation time in audio rooms, in addition to a rough estimate of sound volume in audio rooms. We prove that Sabine's formula for the reverberation time TR is fairly accurate but fails in the computation of the non-uniform sound energy density field whereas the proposed techniques can do it with high precision and speed. Recently, some essays have appeared in new papers based on sound scattering theory which applies digital resolution techniques to resolve the reverberation time TR of sound diffusion PDEs and the sound density field distribution in the sound space of a 3D room, but unfortunately without significant success. The numerical solution of the chains of matrix B has been used successfully to solve the Poisson and Laplace PDE as well as the heat diffusion equation. Here we use the B chain techniques as a real break with the problem of the time dependent sound field in 3D geometric space. We predict the design of audio rooms in two examples of cubic rooms. It has proven effective to provide a reformulation of the Sabin reverberation time equation in addition to calculating the non-uniform field of sound energy density with high precision and speed.


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